CN110704805B - A Cracking Early Warning Method for Prestressed Concrete Girder Bridges Based on Live Load Strain - Google Patents

Abstract

The invention discloses a pre-stressed concrete beam bridge cracking early warning method based on live load strain, which comprises the following steps: collecting strain influence line amplitude data of a bridge member when a vehicle passes each time, and drawing a frequency histogram of the strain influence line amplitude data; fitting vertex coordinates of each rectangular histogram of the strain influence line amplitude data frequency histogram by using a least square method by taking a Gaussian mixture model as a target function, and normalizing integral values of the fitting function in a negative infinite interval to a positive infinite interval; determining a boundary value of each peak interval in the Gaussian mixture model function, and performing data clustering on the amplitude data of the strain influence line according to the boundary value of each interval; and taking the data cluster with the maximum mean value as a strain influence line amplitude data cluster under the action of heavy vehicles, taking a strain value corresponding to the cumulative distribution function of the data cluster at a specific guarantee rate as an early warning index for reflecting concrete cracking, and carrying out early warning. Compared with the prior art, the method is accurate and reasonable, has definite physical significance and comprehensive consideration factors.

Description

A Cracking Early Warning Method for Prestressed Concrete Girder Bridges Based on Live Load Strain

technical field

The invention belongs to the field of performance monitoring, detection, early warning and evaluation of existing bridge structures, and is a cracking early warning method for prestressed concrete beam bridges based on live load strain. Cracking early warning method for prestressed concrete girder bridges based on test data.

Background technique

Prestressed concrete girder bridges are commonly used in the design and construction of medium and small-span bridges on China's transportation network, and concrete cracking is the main manifestation of performance degradation during service. With the development of testing technology, data-driven online monitoring and early warning of bridge structural cracking diseases has become possible. Since the vehicle-mounted strain influence line has a clear signal starting point, it can accurately calibrate and quantify the structural load effect, and reflect the long-term performance evolution process of the structure.

At present, in the fields of civil engineering and transportation, there are few methods for early warning of cracking of prestressed concrete beam bridges based on test data, and there are even fewer related methods for long-term and real-time early warning of bridges based on sensor time series data. Commonly used methods are as follows: (1) Cracking defects are found based on manual inspection results: This method involves bridge management personnel approaching the bridge prone to cracking, observing apparent concrete defects, and reporting to technicians for later maintenance and reinforcement work , this method relies on the labor and subjective judgment of the bridge maintenance personnel. It is not only time-consuming and labor-intensive but also dangerous to approach the susceptible location, which is an uneconomical method; (2) directly judge whether cracking is based on the test strain data: this method uses bridge During the monitoring and detection process, the strain value measured by the sensor is converted into the stress value (the elastic modulus of concrete is known). When the stress value is greater than the limit/design tensile strength given in the code, it is determined that the concrete structure is cracked. This method is too ideal , There are too few considerations (for example, the strain caused by temperature will not produce stress equivalently), and the prestressed structure is allowed to work with cracks, and the microcracks under heavy load will be closed due to the prestress effect after the load disappears , so this method lacks rationality; (3) Cracking disease identification through image data: This method usually uses neural network deep learning of the characteristics of cracking images to identify whether there are cracks in the images obtained by high-definition cameras and UAVs. Although this method Reasonable and reliable, but the technical threshold is high, and the image data is not the usual test data in structure monitoring and detection.

Therefore, it is necessary to develop a method with clear physical meaning, low technical threshold, and easy application and implementation for commonly used sensor time series data, so as to realize the early warning of cracking in existing prestressed concrete girder bridges.

Contents of the invention

The technical problem to be solved by the present invention is to provide a prestressed concrete girder bridge cracking early warning method based on live load strain, which can realize cracking disease early warning of existing prestressed concrete girder bridges based on live load strain data.

In order to solve the problems of the technologies described above, the technical solution adopted in the present invention is:

A prestressed concrete girder bridge cracking early warning method based on live load strain, comprising the following steps:

(1) Collect the time history of the strain influence line of each component of the bridge when the vehicle passes each time, extract the amplitude data of each strain influence line time history, accumulate a certain amount of strain influence line amplitude data, and draw the long-term strain influence line amplitude Frequency histogram of the data;

(2) Taking the mixed Gaussian model as the objective function, using the least squares method to fit the vertex coordinates of each rectangular histogram of the strain influence line amplitude data frequency histogram, and normalizing the integral value of the fitting function in the range from negative infinity to positive infinity is 1, and check its goodness of fit;

(3) Determine the boundary value (trough or inflection point) of each single peak interval in the mixed Gaussian model function according to each peak value of the corresponding mixed Gaussian model, and carry out the data of the amplitude data of the strain influence line according to the boundary value of each single peak interval Clustering to form multiple data clusters;

(4) The data cluster corresponding to the single peak interval with the largest average value in the mixed Gaussian model is used as the strain influence line amplitude data cluster under the action of heavy vehicles, and the cumulative distribution function of the data cluster corresponds to the strain value at a specific guarantee rate As an early warning index reflecting concrete cracking, this index is further compared with the limit value of the ultimate tensile strain specification of the concrete material and the early warning is realized.

As a preference of the present invention, the step (1) step is specifically:

(1.1) Collect the strain influence line time history of each component of the bridge when the vehicle passes each time, and each strain measuring point independently extracts the amplitude data of each strain influence line time history and stores it;

(1.2) Draw the respective frequency histograms based on the long-term data of the amplitude of the strain influence line of each strain measuring point sensor.

In a preferred embodiment, the step (2) includes:

(2.1) Take the mixed Gaussian model as the objective function:

Using the method of least squares:

min(∑||f(x _j )-y _j ||)

The vertex coordinates of each rectangular histogram of the fitting strain influence line amplitude data frequency histogram, the Y-axis coordinate of the vertex is the frequency of each rectangular histogram, and the X-axis coordinate of the vertex is the median value of the strain interval of each rectangular histogram;

(2.2) Integrate the fitted mixed Gaussian model function over the interval from negative infinity to positive infinity, and normalize the integral value of the function to 1. According to the integral principle, the normalized coefficient of the integral function can be directly moved into the integral symbol , used as the normalization coefficient of the mixed Gaussian model function;

(2.3) The normalized mixed Gaussian model function is used as the probability density function of the strain influence line amplitude, and its integral function is used as the probability distribution function of the strain influence line amplitude, and the probability distribution function is tested by general methods such as the Kolmogorov-Smirnov test goodness of fit.

As preferred of the present invention, the concrete steps of described step (3) are:

(3.1) Determine the boundary value of each single peak interval in the mixed Gaussian model function according to each peak value of the corresponding mixed Gaussian model. The boundary value usually takes the valley point (minimum value point) between each wave peak. When there is no valley point Then take the inflection point between the mean values of the Gaussian function corresponding to the two single peak intervals;

(3.2) Cluster the amplitude data of the strain influence line according to the boundary value of each single peak interval to form multiple data clusters based on the mixed Gaussian model.

As preferred of the present invention, the step (4) includes:

(4.1) The data cluster corresponding to the single peak interval with the largest average value in the mixed Gaussian model is used as the strain influence line amplitude data cluster under the action of heavy vehicles;

(4.2) Integrate the Gaussian function (usually only one Gaussian function) corresponding to the data cluster over the interval from negative infinity to positive infinity, and normalize the function integral value to 1:

The normalized Gaussian function is used as the probability density function of the amplitude of the heavy-vehicle strain influence line, and its integral function is used as the probability distribution function of the amplitude of the heavy-vehicle strain influence line;

(4.3) The strain value (α) corresponding to the probability distribution function (cumulative distribution function) of the amplitude of the strain influence line of the heavy vehicle at a specific guarantee rate (β, such as 95% for β) is used as an early warning index reflecting concrete cracking:

In the formula, P(x≤α) is the probability of greater than or equal to α in the amplitude data of the strain influence line of the heavy vehicle, which is equal to the function value of the cumulative distribution function (F _K (x≤α)); the index α and the concrete material Compared with the code limit of ultimate tensile strain (obtained by dividing the ultimate tensile strength or design tensile strength in the code by the modulus of elasticity of the concrete material), as the bridge gradually deteriorates, the value of α will slowly approach and then exceed the code limit , when α is greater than the specification value, an alarm is issued.

Compared with the prior art, the present invention has the following beneficial effects:

(1) The prestressed concrete girder bridge cracking warning method proposed by the present invention is based on the vehicle-mounted strain influence line amplitude data, and the vehicle-mounted strain amplitude is directly related to the concrete tensile stress, and the cracking of the structure is mainly produced by the concrete tensile stress, Therefore, it is very reasonable to use the statistical value of the vehicle-mounted strain amplitude data to calculate the early warning index. The method has a clear physical meaning and is convenient for bridge management and maintenance personnel to understand and implement.

(2) The implementation process of the present invention is basically based on the statistical analysis and calculation of test data, and there are few empirical factors. Any technician with a certain mathematical and statistical foundation can realize the prestressed concrete based on live load strain according to this patent Early warning method for girder bridge cracking. The method has strong feasibility and is convenient for wide popularization and application.

3) The logic of the method is strict and the considerations are comprehensive. The present invention proposes to use the statistical parameters of the vehicle-mounted strain amplitude data to realize the cracking warning of the prestressed concrete beam bridge. The vehicle-mounted strain influence line has a clear signal starting point (zero point), and its amplitude can be accurately Calibrate and quantify the load effect, and also exclude the influence of temperature changes on the strain test value. The method is based on strict logical inference and excludes possible interference factors.

Description of drawings

Fig. 1 is the flowchart of the method of the present invention.

Figure 2 is the histogram of the amplitude and frequency of the strain influence line and its fitting with the mixed Gaussian model.

Figure 3 is a schematic diagram of the clustering of the amplitude data of the vehicle strain influence line.

Fig. 4 is a schematic diagram of cracking warning based on the probability characteristics of the amplitude data cluster of the strain influence line of the heavy vehicle.

detailed description

The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.

As shown in Figure 1, the embodiment of the present invention discloses a prestressed concrete girder bridge cracking warning method based on live load strain, which mainly includes the following steps:

Step 10): Collect the time history of the strain influence line of each component of the bridge when the vehicle passes each time, and independently extract and store the amplitude data of each strain influence line time history at each strain measuring point; based on the strain influence of each strain measuring point sensor Line amplitude long-term data plots their respective frequency histograms.

Step 20): Take the mixed Gaussian model as the objective function:

Using the method of least squares:

min(∑||f(x _j )-y _j ||)

The vertex coordinates of each rectangular histogram of the fitting strain influence line amplitude data frequency histogram, the Y-axis coordinate of the vertex is the frequency of each rectangular histogram, and the X-axis coordinate of the vertex is the median value of the strain interval of each rectangular histogram; the fitted The mixed Gaussian model function is integrated over the interval from negative infinity to positive infinity, and the integral value of the function is normalized to 1. According to the integral principle, the normalized coefficient of the integral function can be directly moved into the integral symbol and used as a mixed Gaussian model The normalization coefficient of the function; the normalized mixed Gaussian model function is used as the probability density function of the strain influence line amplitude, and its integral function is used as the probability distribution function of the strain influence line amplitude, using general methods such as the Kolmogorov-Smirnov test Tests the goodness of fit of a probability distribution function.

Step 30): According to the peak value of each peak of the corresponding mixed Gaussian model, determine the boundary value of each single peak interval in the mixed Gaussian model function, the boundary value usually takes the valley point (minimum value point) between each wave peak, and there is no valley point In this case, the inflection point between the mean values of Gaussian functions corresponding to two single peak intervals is taken; the strain influence line amplitude data is clustered according to the boundary value of each single peak interval to form multiple data clusters based on the mixed Gaussian model.

Step 40): use the data cluster corresponding to the single peak interval with the largest average value in the mixed Gaussian model as the strain influence line amplitude data cluster under the action of the heavy vehicle; the Gaussian function corresponding to the data cluster (usually only contains 1 Gaussian function ) is integrated over the interval from negative infinity to positive infinity, and the integral value of the function is normalized to 1:

The normalized Gaussian function is used as the probability density function of the amplitude of the line affected by the strain of the heavy vehicle, and its integral function is used as the probability distribution function of the amplitude of the line affected by the strain of the heavy vehicle; the probability distribution function of the amplitude of the line affected by the strain of the heavy vehicle ( That is, the cumulative distribution function) at a specific guarantee rate (β, such as 95% for β) corresponds to the strain value (α) as an early warning indicator reflecting concrete cracking:

In the formula, P(x≤α) is the probability of greater than or equal to α in the amplitude data of the strain influence line of the heavy vehicle, which is equal to the function value of the cumulative distribution function (F _K (x≤α)); the index α and the concrete material Compared with the code limit of ultimate tensile strain (obtained by dividing the ultimate tensile strength or design tensile strength in the code by the modulus of elasticity of the concrete material), as the bridge gradually deteriorates, the value of α will slowly approach and then exceed the code limit , when α is greater than the specification value, an alarm is issued.

Example 1:

The following is an example of the long-term data of the vehicle-mounted strain influence line amplitude obtained by the longitudinal strain sensor of a certain span of a 25-meter prestressed concrete composite box girder bridge of a certain box girder floor of the Lieshi River Bridge in Jiangsu Province to illustrate the specific implementation process of the present invention.

(1) Collect the time history of the longitudinal strain influence line of a box girder floor of the bridge each time a vehicle passes, extract and store the amplitude data of each strain influence line time history, and draw the respective frequency histograms based on the long-term data of the strain influence line amplitude As shown in Figure 2, the frequency histogram in this example takes 200 rectangular histograms in the range of about 0-70με.

(2) With the mixed Gaussian model as the objective function, the least squares method is used to fit the vertex coordinates of each rectangular histogram of the amplitude data frequency histogram of the strain influence line. The fitted Gaussian distribution model has three obvious peaks, of which the first The first peak contains 2 Gaussian functions, and the second and third peaks contain 1 Gaussian function (as shown in Figure 2) respectively; the mixed Gaussian model function of fitting is integrated on the interval from negative infinity to positive infinity, and The integral value of the function is normalized to 1; the normalized mixed Gaussian model function is used as the probability density function of the strain influence line amplitude, and its integral function is used as the probability distribution function of the strain influence line amplitude, and the Kolmogorov-Smirnov test method is used The goodness of fit of the fitted probability distribution function was tested at a significant level of 0.05.

(3) According to each peak value of the corresponding mixed Gaussian model, determine the boundary value of each single peak interval in the mixed Gaussian model function (the valley value circled in Figure 2); the strain influence line amplitude data is divided into each single peak Data clustering is performed on interval boundary values to form three data clusters based on the mixed Gaussian model (as shown in Figure 3).

(4) Use the data cluster 3 corresponding to the third peak in the mixed Gaussian model as the strain influence line amplitude data cluster under the action of heavy vehicles; integrate the Gaussian function corresponding to data cluster 3 on the interval from negative infinity to positive infinity , and the function integral value is normalized to 1, the normalized Gaussian function is used as the probability density function of the amplitude of the strain influence line of heavy vehicles, and its integral function is used as the probability distribution function of the amplitude of the influence line of heavy vehicle strain; The strain value (α) corresponding to the probability distribution function (i.e. the cumulative distribution function) of the amplitude of the strain influence line of the heavy vehicle at the 95% guarantee rate is used as an early warning index reflecting concrete cracking, and the value of the early warning index α (in this example, α = 38.93με) is compared with the ultimate cracking strain of C50 concrete material 76.52με (converted from the ultimate tensile strength in the specification) and the design cracking strain of 54.78με (converted from the design tensile strength in the specification) (as shown in Figure 4) ; When α is greater than the design cracking strain, a weak alarm is issued, and when α is greater than the ultimate cracking strain, a strong alarm is issued.

The above embodiments are only further specific descriptions of the solutions of the present invention. After reading the embodiments of the present invention, modifications and replacements to various equivalent forms of the present invention by those skilled in the art all belong to the protection defined in the claims of the present application. scope.

Claims (5)

1. a prestressed concrete girder bridge cracking early warning method based on live load strain, is characterized in that, comprises the steps: (1) Collect the time history of the strain influence line of each component of the bridge when the vehicle passes each time, extract the amplitude data of each strain influence line time history, accumulate a certain amount of strain influence line amplitude data, and draw the long-term strain influence line amplitude The frequency or frequency histogram of the data; (2) With the mixed Gaussian model as the objective function, the least square method is used to fit the vertex coordinates of each rectangular histogram of the frequency of the strain influence line amplitude data or the frequency histogram, and the integral value of the fitting function in the range from negative infinity to positive infinity is returned to One into 1, and check its goodness of fit; (3) Determine the boundary value of each single peak interval in the mixed Gaussian model function according to the peak value of each peak of the corresponding mixed Gaussian model, and perform data clustering on the amplitude data of the strain influence line according to the boundary value of each single peak interval to form a multiple a data cluster; (4) The data cluster corresponding to the single peak interval with the largest average value in the mixed Gaussian model is used as the strain influence line amplitude data cluster under the action of heavy vehicles, and the cumulative distribution function of the data cluster corresponds to the strain corresponding to the specific guarantee rate β The value α is used as an early warning indicator reflecting concrete cracking,

In the formula, P(x≤α) is the probability of greater than or equal to α in the amplitude data of the strain influence line of the heavy vehicle, which is equal to the function value of the cumulative distribution function F _K (x≤α); Comparing the standard limit value of tensile strain and realizing early warning. 2. the prestressed concrete girder bridge cracking early warning method based on live load strain according to claim 1, described step (1) is specially: (1.1) Collect the strain influence line time history of each component of the bridge when the vehicle passes each time, and each strain measuring point independently extracts the amplitude data of each strain influence line time history and stores it; (1.2) Based on the long-term data of the strain influence line amplitude data of each strain measuring point sensor, draw the respective frequency or frequency histogram. 3. the prestressed concrete girder bridge cracking early warning method based on live load strain according to claim 1, comprising in the described step (2): (2.1) With the mixed Gaussian model as the objective function, the least square method is used to fit the vertex coordinates of each rectangular histogram of the frequency or frequency histogram of the strain influence line amplitude data. The Y-axis coordinates of the vertices are the frequency or frequency of each rectangular histogram, and The X-axis coordinate of is the median value of the strain interval of each rectangular histogram; The general expression of the mixed Gaussian model is:

The general formula for the method of least squares is: min(∑||f(x _j )-y _j ||) (2.2) Integrate the fitted mixed Gaussian model function over the interval from negative infinity to positive infinity, and normalize the integral value of the function to 1. The normalized coefficient of the integral function can be directly moved into the integral symbol and used as The normalization coefficient of the mixture Gaussian model function; (2.3) The normalized mixed Gaussian model function is used as the probability density function of the strain influence line amplitude, and its integral function is used as the probability distribution function of the strain influence line amplitude, and the probability is tested by chi-square test and Kolmogorov-Smirnov test method Goodness of fit of the distribution function. 4. the prestressed concrete girder bridge cracking early warning method based on live load strain according to claim 1, described step (3) is specially: (3.1) Determine the boundary value of each single peak interval in the mixed Gaussian model function according to the peak value of each peak of the corresponding mixed Gaussian model. The boundary value is the valley point between each peak, and when there is no valley point, two single peak intervals are taken The inflection point between the means of the corresponding Gaussian function; (3.2) Cluster the amplitude data of the strain influence line according to the boundary value of each single peak interval to form multiple data clusters based on the mixed Gaussian model. 5. the prestressed concrete girder bridge cracking early warning method based on live load strain according to claim 1, described step (4) is specially: (4.1) The data cluster corresponding to the single peak interval with the largest average value in the mixed Gaussian model is used as the strain influence line amplitude data cluster under the action of heavy vehicles; (4.2) Integrate the Gaussian function corresponding to the data cluster over the interval from negative infinity to positive infinity, and normalize the integral value of the function to 1:

The normalized Gaussian function is used as the probability density function of the amplitude of the heavy-vehicle strain influence line, and its integral function is used as the probability distribution function of the amplitude of the heavy-vehicle strain influence line; (4.3) The strain value α corresponding to the specific guarantee rate β of the probability distribution function of the amplitude of the strain influence line of the heavy vehicle is used as an early warning index reflecting concrete cracking:

In the formula, P(x≤α) is the probability of greater than or equal to α in the amplitude data of the strain influence line of the heavy vehicle, which is equal to the function value of the cumulative distribution function F _K (x≤α); the index α and the limit of the concrete material are drawn When α is greater than the standard value, it means that the live load strain of the test has frequently exceeded the limit, and an alarm needs to be sent to the management unit at this time.

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